The present invention relates to fluid flow analog computers or systems in contrast to the electric flow analog computers. It particularly relates to physical components and methods for building up and the process of utilizing such systems. This invention in particular uses the potential head and the flow of any fluid as the input signals to the fluid analog computer. There are two physical components or basic units, which make up the main parts of the invention, namely the friction units (FU) and the reservoir units (RU). The flow of the fluid through any friction unit causes loss of potential head, while the reservoir unit stores or releases the fluid. The large number of basic units arranged in various configurations makes possible the construction of many liquid analog computers, the subject of the present invention. Different flow and/or potential head signals as inputs will result in observable and measurable response signals in the system, thereby allowing the solution of many problems. These problems are mainly defined by differential equations.
There are a few types of analog computers and analog models, but to the inventor's knowledge there are no analog computers which use liquids as the flowing medium. There is an analog model, which uses liquid flow in a thin slot between two smooth plates. This is the so-called Hele-Shaw model which is mathematically similar to the liquid flow in a two dimensional potential flow. On the other hand and almost in all cases an analog computer, which is used to solve differential equations, uses electrical flow and electrical circuits.
In the present invention fluid circuits comprising friction units and reservoir units are utilized to construct fluid analog computers for the solution of real world problems defined by differential equations. In addition to the friction units and reservoir units, which make up the basic physical components of the systems, the fluid analog computer may contain at least one terminal reservoir unit (TRU). The terminal reservoir unit may be a simple constant-level overflow device. The flow medium, that flows through the basic units, may be any type of fluid such as oil, water, gas, air, etc.. The friction unit consists of any device that resists the flow of fluids. The laminar, transient and turbulent flow of any fluid through the friction unit causes loss of potential head. In one preferred embodiment, the friction unit consists of a tube filled with granular material. There are many other types and forms of friction units suitable to be used in the fluid analog computer. The reservoir unit consists of any device capable of storing or releasing the fluid. The change of the liquid level or fluid pressure in reservoir units will change the rate of fluid flow through the friction units. In one preferred embodiment the reservoir unit is a transparent hollow cylinder. The basic units, the friction and reservoir units, are arranged and interconnected in a variety of configurations. This process of arranging and interconnecting various basic units forms one of the backbones of the present invention.
In operation any continuous, discontinuous, constant, variable, periodic, etc., type of flow or head may be imposed on one or more of the reservoir units. These forcing functions, sources and/or sinks may be obtained by special pumps, outputs of other fluid analog computers, and special devices such as springs and machines producing vertical (up and down) motions. The response signals, in terms of fluid flows or fluid pressures, produced by the specific configuration of the physical components of the system and by the input signals are definable by differential equations. The solutions to these differential equations are the measurable response signals produced by the present invention.
It is an object of the present invention to provide fluid analog computers of exceedingly simple conception, construction and operation. The primary advantage of the present invention is that one of the response signals or variables (the potential head) is readily observable by the naked eye in the fluid analog computer. Therefore the variables or the solutions to the differential equations may be sensed and visualized. The visualization and observation of the solution assigns a great value to the invention as an instrument for educational and instructional purposes. It is also a great process for understanding, investigating and designing real world problems and systems by solving the applicable differential equations.
One of the principle objectives and advantages of the fluid analog computer is that it is readily adaptable to existing and widely available instrumentation, including digital computers, for measuring, indicating, recording and monitoring the variables and for furthers computations.
Another advantage is the capability of the system to be frozen or stopped at any moment in time for further investigation of a particular state. In contrast one cannot stop the electro-analog computers.
A further advantage of the fluid analog computer is its capability to extend the number of basic units in one or more directions. This creates other independent variables, such as distance, in addition to time. In one version, the extension of the basic units to all three spatial directions will produce an analog model suitable for the simulation of many complicated real world problems, like the flow of liquids in porous media.
Still another objective of the present invention is to observe and record the solution of nonlinear differential equations, some of which are very difficult and/or very costly to solve by mathematical means.
An extremely valuable advantage of the fluid analog computer, is that the fluid levels are observable directly in their natural state. This advantage enables one to intuitively visualize, sense and predict the solution to many problems defined by differential equations.
It is an object of the invention to provide improved elements and arrangements thereof in an apparatus for the purposes described which is inexpensive, dependable and fully effective in accomplishing its intended purposes.
While one skilled in the art would appreciate that fluid encompasses liquids and gases, the terms fluid, liquid, and gas will be used interchangeable and understood that the apparatus according to the present invention can operate with either regardless of the term used to explain an embodiment of the invention. And likewise, the respective pressure and potential head developed by these fluids will also be used interchangeably and should not be read as a specific limitation inherent in the system.